In the left panel of figure REF  we plot the mean \(\langle X_{max} \rangle \)  as measured by Auger and TA and in the right panel we plot the event-by-event fluctuations of the shower maximum distribution \(\sigma (X_{max})\) , the TA data are corrected subtracting detectors effects as discussed in [1]}. For comparison the prediction of \(\langle X_{max} \rangle \)  and \(\sigma (X_{max})\)  in the case of a pure proton and a pure iron composition are displayed. The expected behaviour of \(\langle X_{max} \rangle \)  and \(\sigma (X_{max})\)  differs depending on the hadronic interaction model used, in figure REF  we plot three different models: EPOS-LHC (solid lines), Sybil 2.3 (dashed lines) and QGSJetII-04 (dotted lines) (see [1]}, [3]} and references therein).
